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We study theoretically quantum statistical and spectral properties of theresonance fluorescence of a single atom or system with angular momentum $J=1/2- J'=1/2$ driven by a monochromatic linearly polarized laser field, due toquantum interference among its two antiparallel, $\pi$ transitions. A magneticfield parallel to the laser polarization is applied to break the degeneracy(Zeeman effect). In the nondegenerate case, the $\pi$ transitions evolve atdifferent generalized Rabi frequencies, producing quantum beats in theintensity and the dipole-dipole, intensity-intensity, and quadrature-intensitycorrelations. For a strong laser and large Zeeman splitting the beats have meanand modulation frequencies given by the average and difference, respectively,of the Rabi frequencies, unlike thebeats studied in many spectroscopic systems,characterized by a modulated exponential-like decay. Further, the Rabifrequencies are those of the pairs of sidebands of the Mollow-like spectrum ofthe system. In the two-time correlations, the cross contributions, i.e., thosewith products of probability amplitudes of the two $\pi$ transitions, have alesser role than those from the interference of the probability densities. Incontrast, there are no cross terms in the total intensity. We also considernonclassical and non-Gaussian properties of the phase-dependent fluorescencefor the cases of weak to moderate excitation and in the regime of beats. Thefluorescence in the beats regime is nonclassical, mainly from third-orderdipole fluctuations, which reveal them to be also strongly non-Gaussian, andtheir quadrature spectra show complex features around the Rabi frequencies. Forsmall laser and Zeeman detunings, a weak to moderate laser field pumps thesystem partially to one of the ground states, showing slow decay in the twotime correlations and a narrow peak in the quadrature spectra.

Quantum interference in the resonance fluorescence of a $J=1/2$-$J'=1/2$ atomic system: Quantum beats, nonclassicality, and non-Gaussianity